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Russian stocks have been more yawn-inducing than awe-inspiring in the past year, but prepare for them to wake up in the New Year.

The MSCI Russia Index has gained just 6.9% this year, a little more than half of the MSCI Emerging Markets Index's 12.3% rise. And predictions of Russia's rally have proved premature in recent years, causing some investors to lose patience. Investors have pulled $48 million out of actively managed Russia funds this year, even as emerging-market stock funds generally have attracted $8 billion.

But Russia could surprise many investors in 2013. The two biggest reasons: Russia's stocks are cheap, and its government is finally embarking on some much-needed reform.

That isn't to say that the low valuations aren't deserved. Russia is notorious for treating investors as an afterthought, and it isn't so easy on local business, either. The bribes required to get electricity or building permits have placed Russia at 112th of 185 countries in the World Bank's Ease of Doing Business rankings. "Reforms need to happen," says Simon Mandel, head of emerging Europe equities at Auerbach Grayson, a New York brokerage firm that deals predominantly with international stocks. "But given the course of Russian history, they won't happen quickly."

Still, Russia has made investing notably easier for foreigners, says Bruce Bower, a portfolio manager at Verno Capital. It recently agreed to set up a central depository, making the trading of Russian securities far easier. At the same time, the nation's central bank has been doing more to boost its credibility by targeting inflation and letting the ruble float more freely. Both should make Russia a more attractive locale for investor cash.

But a resolution of the U.S. fiscal cliff—the guaranteed tax hikes and budget cuts go into effect on Jan. 1—would really juice the Russian stock market, says Michael Harris, an equity strategist at Bank of America Merrill Lynch in London. Right now, the uncertainty in the U.S. has some investors concerned that oil prices could fall, not a good catalyst for Russian stocks, whose prices are generally linked to the price of crude oil. The MSCI Russia Index has a correlation of 72% with the price of Brent crude, a classification of sweet, light crude.

But once the cliff passes, "the perception of risk will diminish," Harris says, and oil will find a floor. "Even if the market is not flying, Russia will work against this global backdrop."

Russian stocks have generally outperformed following disappointing years, Harris says. Still, it wouldn't hurt to get exposure to Russian companies outside the oil and gas sector. Analyst favorites include Sberbank of Russia (SBER.Russia), one of the country's largest banks, and mobile-phone operators OJSC MegaFon (MFON.Russia) and Mobile Telesystems OJSC (MTSS.Russia).

The Market Vectors Russia ETF has returned 10% so far in 2012 and has an annual fee of 0.62%. The downside: It has 42% of its portfolio invested in the energy sector. But if investors do unleash their "animal spirits," it may not matter, says Société Générale's Benoit Anne. "If we start 2013 with a strong rally, I can see the Russian market taking off nicely."